When wiring my guitar pickup, I connected the ground wire to the ground of the output jack. After hooking that up, I would hear a hum unless I soldered a wire from the metal bridge of the guitar (where the strings enter the guitar body) to the same ground of the output jack. Why did I need to connect the bridge to ground?
The 'ground' of the output jack is actually a shield (and probably connected to chassis ground). It prevents outside electric fields (especially the 60Hz hum) from capacitively coupling into the audio signals inside the cable and jack. By soldering the bridge to the shield, you are extending the shield around the pickups.
Noise can couple into circuits capacitively (via electric fields) or inductively (via magnetic fields). Shielding stops electric fields. Its also good not to turn cabling into an antenna (which could have also been happening with your setup.
Magnetic fields are more difficult because they can only be attenuated by materials. The best thing to do is not create loops which make antennas and avoid mutual coupling (every wire with current creates a magnetic field)
An ideal shield looks like the bottom diagram, since you can't put a shield all the way around the pickups, grounding it is a close second.
Point 1 is that your body can pick up a lot of interference including AC power voltages. These are capacitively connected to your body from the wiring in your home. Point 2 is that the strings and bridge form a fairly decent plate of a capacitor. When you touch this "plate" and this "plate" is floating, you are applying your body's received AC voltage to it.
At these fairly low frequencies, the outer metal screen of a guitar pickup (if it has one as per gibson guitars) is not a great shield against the influences received by the body. This means you get another capacitive connectivity to the coils in the pick up.
If the bridge is grounded to the jack, when you touch the strings, the voltage that is picked up by the body is shunted away to local guitar ground and the interference is much reduced.
Gibson guitars are more resilient to this situation because of the more metalized pick up. Fender guitars can be more problematic. This has nothing to do with the use of humbucking pick ups on Gibson guitars; this is an electric field influenced problem.